Three-weighted torsion balance



Dec. 3, 1929. E. KOGBETLIANTZ THREE-WEIGHTED TORSION BALANCE Filed May 51, 1927 Patented Dec. 3, 1929 UNITED STATES PATENT OFFIC ERVAN D KOGZBETLIANTZ, OF PARIS, FRANCE THREE-WEIGHTED TORSION BALANCE Application filed May 31, 1927, Serial No. 195,547, and in France June 14, 1926.

The two-Weighted torsion balance of Coulomb modified by Eotvos is beginning to play an important part for geological survey because its use often does away with the very expensive drillingwork required.

In order to discover the structure of underlying formations with a torsion balance, curves connecting points where the vertical component of gravity isthe same are traced.

This vertical component is calculated by ascertaining the increase of the component I from one point to another distant therefrom by one centimeter for instance, this increase being calculated from the data given by the balance during the observations made at each pomt.

At each point it is suflicient to determine the values of the gradients of gravity 3 which is secured an equal mass at a certain distance below the beam.

Unfortunately such balances only give the magnitudes 1 g 1 2 40 dxdz an dydz together with the other derivative functions (1 17 dU (1 v dacdy an in ra I unkn Therefore it is necessary, when it is desired to obtain d U d d l7 dmdz dydz to solve a system of linear equations of the first order with four unknowns which are the four derivative functions designed by the following symbols As the well known theory of torsion balances 60 proves, the following is the equation of equilibrium for one beam directed in the azimuthA cos A- U, sin A) T being the angular displacement of the beam, m the mass secured to the ends of each beam, 72. the difference in height of themasses m of each beam, 2 l the length of the beam and t the coeflicient of torsion of the platinum Wire. K is the moment of inertia of the whole (beam and masses) with reference to the axis of the platinum wire (see Ambronns work Methoden der angewandten Geophysik 1926, page 20). v The zero of the scale varies by reason of the variations in temperature; there are altogether five unknowns to wit:

'the zero of the scale of torsion and the four abovementioned derivative functions. Therefore a balance with only one beam requires in each point at least five observations in five different azimuths;

With two beams as commonly used in torsion balances three observations would give six equations allowin to determine the six owns U U U and the two zeros of the scales corresponding to the two 90 a torsion wires. In practice four observations are necessary in view'of obtaining an extra control equation.

Due to the interference of the two superfluous unknowns U and U the number of observations at each point must necessarily be increased whereby the accuracy of the measurement/sis diminished.

These serious drawbacks are intrinsic drawbacks of the beam with two masses used exclusively up till now in torsion balances, as they are due to the number of masses which is the same in all forms of execution of such apparati (Schweydar-Bamberg, Siiss, liecgzer, Oerfling, Haalek balances and the 1' e Now I remove these drawbacks by using beams provided with n equal masses, n being superior to 2, secured to or hanging from the ends of n arms. of equal length forming to-:

gether a star-beam showing 1?. arms disposed symmetrically round its suspension point. The n masses are secured to or hang from the beam at different heights h, k h below the ends of the corresponding arms thereof.

v The equation of equilibrium of such a'beam contains only the unknowns Ux and U The most simple case and the easiest to execute is that shown on appended drawings by way of example and wherein 11 3.

Fig. 1 isa diagrammatical view of a onebeam torsion balance according to my invention.

Fig. 2 is a similar view of a three-beam torsion balance of the same type. Fig. 3 shows the same balance asexe'cuted in practice.

In this balance each beam is formed by three horizontal rods more;

of equal length l, secured symmetrically to the suspension point of the beam. Three equal masses m are secured to or hang from the apices a. B, c of the equilateral triangle formed by the three ends of the three rods of the beam. I will term U.. and U312 respectively the derivative functions s l Eli dc dy The beam hangs by means of a substantially rigid wire having a coefficient of torsion equal to t.

It is easy to calculate the projections on the axes 0a: and 0y of the forces ofgravity applied to the masses A, B and C.

The force applied to point A has respectively for projectionsv ml cos A U +'ml sin A U. -l-mh U and 777F008 A U -kml sin A U$+mh U...

They are for point B:

and v I ml as (A+120) U..,,+mzsin (A+120) U; and for pointC: .ml cos (A -120) U andmlcos (A120) Ua'y'l' 7 v ml sin (Al-120) U +2mh Uyg Thus their moments with reference to the vertical axis OZ are for A:

me cos 2A. U m2 sin 2A UD-J- mkl (U cosAU sin A) for B:

ml cos (2A+240) Uw' I F V gml sin (2A+240) U and for G:

ml cos (2A-240) U ml (sin (2A- 240 U -l-QmhZ 1],,z cos A120 Uwasln. I Addin these values together, I obtain after simpli cation the total moment N.

N= mm .le 17.. 003.4 0;, sin A).

ml cos (A+l20-) U -l-ml sin (Ad-120) Uwy ml sin (A-120) U...,+je h U...

directed in the azimuth is d v (1 v t. T

dxdz cosA +dydz s1nA T being the angular displacement of the beam and t the coeflicient of torsion of the suspension wire; with one single beam provided with three masses there are three unknowns U U and the position of the zero of the scale. Therefore four observations are necessary including one for a control equat1on. By increasing the number of beams the number of observations necessary in one point is reduced. 1

For instance I may use the balance shown on Fig. 2 provided withthree identical beams each showing 3 divergent rods and three masses. These beams a hang from three sus pension wires b disposed next to each other in such a manner that the three equal masses m borne by the adjacent ends of three arms belonging to three distinct beams are at different levels. Of course these groups of three masses are contained as usual in a vertical tube e in view of eliminating any perturbawire and equal masses the number of which is e ual to the total number of rods and means w ereby the masses hang freely from the end of the corresponding rods the vertical dis- 20 ing the unknowns, one equation serving as a tance between each mass and the beam from which .it hangs being difierent according to the rod considered.

In testimony whereof I have aflixed my signature.

* ERVAND KOGBETLIANTZ.

- tions from outside.

Two observations made with such a balance in two different azimuths ar'e sulficient for ascertaining the values of @311 d i l dmdz dydz at the point considered whereas as explained hereinabove, four measurements are necessary with Eotviiss balance. The number of unknowns is five (U U z and the positions of the three zeros, corresponding to the three beams) and as each measurement provides threeequations, the six e nations obtained by two observations are su oient for ascertain-' control e uatlon.

As to t e execution of such a balance, it is entirely similar to the usual Eotvoss balance with two weights. I prefer though to replace the stationary plate 1n the usual automatic photographic recording method by a very slowly continuously moving plate. This al lows not onlv thestationary luminous spot corresponding to the e uilibrium of each beam to be photographe but also the continuous curve (a damped sinusoid) 'which corresponds to the oscillations of the beam so as to ascertain the position of equilibrium by the mean position of the spot between a number of couples of positions corresponding to the extreme elongations.

What I claim is:

1. A torsion balance comprising a suspension wire, a beam constituted by more than two horizontal rodssecured together angularly spaced by equal amounts one with reference to the other and starting radially from the lower end of the suspension wire and equal masses equal in number to the rods and means whereby the masses are secured to the end of the corresponding rods and at a vertical distance therefrom different for each mass.

2. A torsion balance comprising a suspension wire, a beam constituted by three rods secured together angularly spaced by equal amounts one with reference to the other and starting radially from the lower end of the suspension wire three equal masses and means whereby the masses are secured to-the end of the corresponding rods and at vertical dis,- tance therefrom difi'erent for each mass.

3. A multiple torsion balance constituted by a plurality of suspension wires hanging side by side, similar beamshanging from each suspension wire and each constituted by more than two rods secured together angularly spaced by equal amounts one with reference to the other and starting radially from the 65 lower end of the corresponding suspension 

